In this context, assimilation is a process in which a group of people who have been outside of the mainstream of a society are brought in to that mainstream. (Or at least, it is a process of attempting to do this.) It is a process in which a government or society attempts to reduce the cultural uniqueness of the group so that it can become just another part of mainstream society.
In Australia, assimilation became government policy around the middle of the 20th century. The idea was that policies towards aborigines should change from paternalism to assimilation. In many ways, this was a noble idea in that it called for aborigines to have the same standards of living as other Australians. Paternalistic laws were done away with and more money was spent on education and training for aborigines. However, there was clearly an attempt to do away with indigenous culture and to make aborigines become just like other Australians. The most famous (or infamous) example of this was the policy of taking aboriginal children from their parents so that they would be socialized into mainstream Australian society.
Assimilation, then, was the policy of trying to make aboriginal Australians become just like other Australians regardless of whether they wanted to be changed.